Question

find the equation of the tangent line of f(x)=x^2 when the x-int of the tangent is 2

Answer 1

I know f'(x)=2x, but I'm stuck with the 'x-int of the tangent is 2', does that mean when y=0, x=2?

Answer 2

@amistre64

Answer 3

yes, the tangent line passes thru (2,0)

Answer 4

what can I do next?

Answer 5

let the required point on the curve be (a,b) you have a slope already, a general point, and values for x and y. put them altogether

Answer 6

y = m(x-a)+b

Answer 7

(x-a) because the point is (2,0) right?

Answer 8

f(x)=x^2; for the point (a,b), f(a) = a^2 = b

m = f'(a) = 2a

x = 2
y = 0

0 = 2a(2-a)+a^2 now we can solve for a (and a^2) to determine the equation of the line

Answer 9

I see.. thank you!

Answer 10

youre welcome

there should be 2 tangent lines to the curve that pass thru (2,0)

the line y=0 is one of them, the other is whatever the other root for a is

Answer 11

ok, thanks